I went ahead and ordered a new breech plug. Since I'm shooting loose (Real ffg BP) powder with the "pellet" plug that came with the gun I figured that may not be the best combination for optimum accuracy anyway, so I ordered a BH209 plug for it.
The bore cleaner should be here tomorrow, but the breech plug won't be here until Dec 5. I'll probably wait until I have both items on hand to try a bench session to see if accuracy improves.